Once you are all setup with your Bot you start with zero subscribers.
Fret not! You can still leverage your facebook page activity to gradually increase your subscriber base. There are multiple entry points for a facebook user to become your messenger subscriber like :-
Any user who click 'Send Message' button on your facebook page to interact will become your messenger subscriber.
Enable comment targeting functionality to facilitate engaged users to become your subscriber.
Share your page's m.me link to various marketing channels. This link when clicked opens up your bot chat window. If user chooses to click 'Get Started' button they become your subscriber.
Smugglr Widgets can be strategically placed on your websites to convert users to messenger.